Israel has lifted a ban on UN and foreign aid workers entering Gaza
The BBC is under pressure to air a charity appeal for aid to Gaza after other channels agreed to broadcast it.
Director general Mark Thompson has said by airing the appeal the BBC would risk reducing public confidence in its impartial coverage of the conflict.
But Communities Secretary Hazel Blears urged a review of the decision as 2,000 protested at the BBC's London HQ.
BBC Trust chairman Michael Lyons voiced concerns over political interference in the BBC's editorial independence.
Earlier, rival broadcasters ITV, Channel 4 and Five agreed to broadcast the Disasters Emergency Committee (DEC) appeal. It will be screened for the first time on Monday.
In a blog message on the BBC website explaining the decision, Mark Thompson said: "Inevitably an appeal would use pictures which are the same or similar to those we would be using in our news programmes but would do so with the objective of encouraging public donations.
"The danger for the BBC is that this could be interpreted as taking a political stance on an ongoing story."
When we have turned down DEC appeals in the past on impartiality grounds it has been because of this risk of giving the public the impression that the BBC was taking sides in an ongoing conflict
He stressed the corporation would "continue to cover the human side of the conflict in Gaza extensively across our news services where we can place all of the issues in context in an objective and balanced way".
Earlier on Saturday, police said at least 2,000 protesters gathered outside the BBC's Broadcasting House in central London, and chants of "BBC, shame on you" were heard as a petition was handed in to the corporation.
There were seven arrests at the rally - five people were arrested on suspicion of obstructing police at the Piccadilly Circus junction with Regent Street.
One person was arrested on suspicion of assault of police outside St Martin's in the Field, Trafalgar Sqaure, while another was arrested on suspicion of possession of class A drugs.
Veteran politician Tony Benn, a speaker at the protest, said: "We can't ignore suffering in the interests of what the BBC call impartiality.
"We can't allow others to die when we have an opportunity to save their lives."
Earlier, ITV and Sky had been in agreement with the BBC that they would not air the appeal. But ITV later reversed its decision.
Sky says it is still considering the Disasters Emergency Committee's request.
The DEC - an umbrella organisation for several major aid charities - wants to raise funds for people in need of food, shelter and medicines as a result of Israel's military action in the Gaza Strip.
Previous DEC appeals shown on multiple TV and radio channels have raised millions of pounds for victims of wars and natural disasters.
International Development Secretary Douglas Alexander told BBC Radio 4's Today programme the British public could "distinguish between support for humanitarian aid and perceived partiality in a conflict".
"I really struggle to see in the face of the immense human suffering of people in Gaza... that this is in any way a credible argument," he added.
Tony Benn on the decision by the BBC not to broadcast the appeal
"They [the BBC] still have time to make a different judgement to recognise the immense human suffering."
Shadow international development secretary Andrew Mitchell said it was "clearly a decision for the BBC and other broadcasters " whether they showed the appeal.
But the Conservatives believed it should be played to allow the public to make up their own minds about the appeal, he said.
Liberal Democrat media spokesman Don Foster said the BBC's "disgraceful" decision must be reversed.
"It is unbelievable that the BBC claims to know better than either the government or the 12 major charities that form the DEC about whether aid can get through," he added.
In a letter to the BBC director general on Saturday, BBC Trust chairman Michael Lyons expressed concern that the "level and tone" of some of the political comment was "coming close to constituting undue interference in the editorial independence of the BBC".
He assured Mr Thompson the Trust would "do everything in our power to ensure that you are given the space to make the editorial decisions you feel, after due consideration, are right in the circumstances".
BBC's chief operating officer Caroline Thomson defends the veto
BBC political correspondent Gary O'Donoghue said the corporation was facing "quite a lot of pressure", but its position had been shored up "a little bit" by the Trust's move.
"In other words - a warning to government to say, 'Keep your tanks off our lawn,'" our correspondent said.
Geoffrey Dennis, chief executive of the global humanitarian group Care International, said it was not a time for politics.
"As far as being impartial is concerned, that's our job... we know exactly what we are doing on the ground, there are a lot of people in real danger at the moment."
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